How Do You Calculate the Determinant of This Complex Matrix?

[Helloes]

Homework Statement

I have to find a determinant for
1 2 3 ... n
-1 0 3 ... n
-1 -2 0 ... n
...
-1 -2 -3 ... 0
but I have very little clue how to proceed, because the mathematics material that I was given is very vague about this. Any help would be greatly appreciated.

Homework Equations

The Attempt at a Solution

 

[LawrenceC]

Does -1 -2 -3 ... 0 represent the final row of the matrix meaning the the lowest right member is 0?

 

[I like Serena]

Welcome to PF, Helloes!

The main rule about calculating determinants, is that you can add a multiple of a row to another row, without changing the determinant.
Same thing for columns: you can add (or subtract) a multiple of one column to another column.

Now let's try a couple of determinants.

What is |1|?

What is \begin{vmatrix}1&2\\-1&0\end{vmatrix}?

What is \begin{vmatrix}1&2&3\\-1&0&3\\-1&-2&0\end{vmatrix}?

What is \begin{vmatrix}1&2&3&4\\-1&0&3&4\\-1&-2&0&4\\-1&-2&-3&0\end{vmatrix}?